We have also mentioned that \(V_{\mathrm {mars}}(\cdot )\)  can be viewed as second-order Hardy-Krause variation (anchored at \(\mathbf {0}\) ). Our
estimation strategy can thus be seen as second-order Hardy-Krause
denoising. In [1]}, first-order Hardy-Krause
denoising (i.e., least squares estimation over
functions with bounded Hardy-Krause variation) was studied. First-order
Hardy-Krause denoising leads to piecewise constant fits while
our method leads to MARS fits (linear combinations of
products of ReLU functions of individual variables).
